Cut can be found on the S.S anne after you fight Gary on it, after you fight him go up the stairs right in front of you and talk to the captain, you rub his back and make him feel better. Then he gives you hm01 Cut.
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The HM01 Cut can be given by a person in the house left of the Pokemon Center.
You get Cut in the forest outside Azalea town, you have to find the Charcoal man's Farfetch'ds.
you can find it as an item ball in the route before osuwari city
If you mean HM01 Cut, you can get it from Cutter Man in Rustboro City. His house is beside the Pokemon Center.
You can find Leftovers in Route 12. You will need the move Cut to be able to reach it.